In the last three decades, quantum algorithms have been developed that offer fast solutions to problems in a variety of fields, including number theory, optimization, database search, chemistry, and physics. Krysta Svore of Microsoft Research, Scott Aaronson of MIT, and Matthias Troyer of ETH Zurich discuss the latest breakthroughs in the field of quantum computing and where they might take us. This Research in Focus session was recorded during the 2013 Microsoft Research Faculty Summit.